Results 1 to 10 of about 63 (30)
Estimates for evolutionary partial differential equations in classical function spaces
Forum of Mathematics, Sigma, 2023 We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations.
Alejandro J. Castro +3 more
doaj +1 more source
The agreement between novel exact and numerical solutions of nonlinear models
Partial Differential Equations in Applied Mathematics, 2023 Nonlinear models (NLMs), being an important topic in mathematical physics, have attracted a lot of attention in the international research community because they have numerous uses in human life. These NLMs are typically implemented to illuminate various
Md. Nur Alam, S. M. Rayhanul Islam
doaj
Alexandria Engineering Journal, 2020 In this research, analytical and numerical solutions are studied of a two–dimensional discrete electrical lattice, which is mathematically represented by the modified Zakharov–Kuznetsov equation.
Choonkil Park +4 more
doaj
The probabilistic scaling paradigm [PDF]
arXiv, 2023 In this note we further discuss the probabilistic scaling introduced by the authors in [21, 22]. In particular we do a case study comparing the stochastic heat equation, the nonlinear wave equation and the nonlinear Schrodinger equation.
arxiv
Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3 [PDF]
, 2013 Consider a bilinear interaction between two linear dispersive waves with a generic resonant structure (roughly speaking, space and time resonant sets intersect transversally). We derive an asymptotic equivalent of the solution for data in the Schwartz class, and bilinear dispersive estimates for data in weighted Lebesgue spaces. An application to water
arxiv +1 more source
Random data Cauchy theory for supercritical wave equations I: Local theory [PDF]
, 2007 We study the local existence of strong solutions for the cubic nonlinear wave equation with data in $H^s(M)$, $s<1/2$, where $M$ is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense).
arxiv +1 more source
Random data Cauchy theory for supercritical wave equations II : A global existence result [PDF]
, 2007 We prove that the subquartic wave equation on the three dimensional ball $\Theta$, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in $\cap_{s<1/2} H^s(\Theta)$. We obtain this result as a consequence of a general random data Cauchy theory for supercritical wave equations developed ...
arxiv +1 more source
On Strichartz estimates for Schrödinger operators in compact manifolds with boundary [PDF]
arXiv, 2006 We prove local Strichartz estimates on compact manifolds with boundary. Our results also apply more generally to compact manifolds with Lipschitz metrics.
arxiv
Large time behavior of solutions to a dissipative Boussinesq system [PDF]
arXiv, 2006 In this article we consider the Boussinesq system supplemented with some dissipation terms. These equations model the propagation of a waterwave in shallow water. We prove the existence of a global smooth attractor for the corresponding dynamical system.
arxiv
On multilinear spectral cluster estimates for manifolds with boundary [PDF]
arXiv, 2006 We prove sharp bilinear estimates for Dirichlet or Neumann eigenfunctions in domains in the plane. These are the natural analog of earlier estimates for the boundaryless case of Burq, G\'erard, and Tzvetkov.
arxiv